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MathematicsAlgebraAges 13–14

Simultaneous Equations

Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations

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Simultaneous Equations means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.

Materials: Two simple equation cards; Pencil and scrap paper. 1. Say the goal of Simultaneous Equations in plain words once. 2. Adult solves x+y=5 and x−y=1 by substitution or elimination. 3. Child solves three paired linear systems and checks each pair by substitution. 4. Fresh check: one fresh two-equation system. Record and stop. Done: three correct (x,y) pairs with a check. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.

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Simultaneous Equations practice

Practice key ideas from Simultaneous Equations.

Free · no login · no ads · Practice answers and completion are not saved. Parent observation remains the lesson record.

Learning resources

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PhET Interactive Simulations · Practice link — not the full lesson

Graphing Lines

Open practice (new tab)
Before you open · source notes

Graphing Lines supports hands-on exploration for Simultaneous Equations. Not every lab worksheet.

Free interactive page, no sign-in required for the tested path.

Before you open

Ask the learner what they changed in the sim or page and what they observed.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.

PhET Interactive Simulations. “Graphing Lines.” External page; Gakuva does not copy, host, embed, or redistribute materials.

Unknown — link only

Check understanding

  • Explain that the intersection of two lines represents values satisfying both equations
  • Find the approximate solution to a pair of simultaneous equations by reading a graph
  • Verify a proposed solution by substituting into both equations
“Can your child explain that solving two equations simultaneously means finding the one pair of values that satisfies both at once — and show what that looks like on a graph?”

Curriculum record

Type
Conceptual
Subject
Mathematics
Domain
Algebra
Age range
Ages 13–14

Standards

ccss-math:8.EE.8accss-math:8.EE.8buk-nc-2013:KS3.Maths.Alg.10